Dynamic Touch: Muscles as the Medium

Week 4: Dynamics of Perception & Action

Tehran Davis

Recap: Action-Scaled World

We have seen that we perceive the world in terms of our capabilities.

  • Optic Flow: Where am I going? (Locomotion)
  • Affordances: What can I do? (Climbing, Passing through)
  • Body Scaling: How do I fit? (() numbers)

Today: How do we perceive the world through our body?

The Problem: The Blind Man’s Cane

“If a blind man uses a cane, he feels the sidewalk, not the cane.” — Merleau-Ponty / Gibson

  • Proximal Stimulus: Pressure on the palm of the hand.
  • Distal Perception: The texture and distance of the sidewalk.

How do we perceive the tip of the tool when we are holding the handle?

Three Kinds of Touch

  1. Cutaneous Touch: (Passive)
    • Stimulation of skin (heat, texture, pain).
    • Example: A fly landing on your arm.
  2. Haptic Touch: (Active)
    • Exploratory movement of hands.
    • Example: Identifying a key in your pocket.
  3. Dynamic Touch: (Effortful)
    • Muscular exertion / Wielding.
    • Example: Swinging a tennis racket.

The Wielding Experiment

Solomon & Turvey (1988)

  • Task: Hold a rod behind a curtain. Wield it (wrist only).
  • Question: How long is it?
  • Result: Participants are incredibly accurate ((r^2 = .99)).

Crucial Point: They never see the rod. They never touch the tip. They only feel the forces in the handle.

Hypothesis 1: Is it Mass (Weight)?

If I give you a heavy rod and a light rod, does the heavy one feel longer?

  • Not necessarily.
  • A short, heavy steel rod feels short and heavy.
  • A long, light wooden rod feels long and light.

Conclusion: Mass alone does not specify length.

The Physics of Rotation

When you wield an object, you are rotating it. To rotate an object, you must overcome its resistance to rotation.

Moment of Inertia ((I)): \[ I = m \times d^2 \]

  • (m) = Mass (How heavy is it?)
  • (d) = Distance of mass from axis of rotation (How far away is it?)

Why Distance Matters

Imagine holding a sledgehammer.

  1. Hold the handle: Heavy head is far away ((d) is large). Hard to rotate. Feels Long.
  2. Hold the head: Heavy head is close ((d) is small). Easy to rotate. Feels Short.

The Moment of Inertia specifies the reachability of the object.

The Inertia Tensor ((I_{ij}))

Objects aren’t just lines. They are 3D shapes. You can rotate them in 3 dimensions (Pitch, Yaw, Roll).

The Inertia Tensor is a (3 ) matrix that captures resistance to rotation in all directions.

\[ I = \begin{bmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{yx} & I_{yy} & I_{yz} \\ I_{zx} & I_{zy} & I_{zz} \end{bmatrix} \]

Perception via Dynamics

Physics Perception
Moment of Inertia ((I)) \(\rightarrow\)
Product of Inertia ((I_{xy})) \(\rightarrow\)
Principal Axes \(\rightarrow\)

We detect the invariant physical dynamics (Inertia) to perceive the variant spatial properties (Length).

Application: Tool Use

This is how we use tools.

  • When we pick up a tool, we “probe” its inertia tensor by wielding it.
  • We instantly know “how far it reaches” and “where the heavy part is.”
  • The tool becomes a transparent extension of the body.

Next Class: Thursday

Activity: “The Wielding Game”

  • You will wield unseen objects.
  • You will predict their length and shape.
  • We will see if you are sensitive to the Inertia Tensor.

Reading: * Turvey & Carello (1995) * Blau & Wagman Chapter 8